The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Dropping a variable(s) and specification bias.
When faced with severe multi-
collinearity, one of the “simplest” things to do is to drop one of the collinear variables.
30
Mark B. Stewart and Kenneth F. Wallis, 
Introductory Econometrics,
2d ed., John Wiley & Sons, A
Halstead Press Book, New York, 1981, p. 154.
31
J. Tobin, “A Statistical Demand Function for Food in the U.S.A.,” 
Journal of the Royal Statistical
Society,
Ser. A, 1950, pp. 113–141.
32
For a thorough discussion and application of the pooling technique, see Edwin Kuh, 
Capital Stock
Growth: A Micro-Econometric Approach
, North-Holland Publishing Company, Amsterdam, 1963,
Chapters 5 and 6.
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Part Two
Relaxing the Assumptions of the Classical Model
Thus, in our consumption–income–wealth illustration, when we drop the wealth variable,
we obtain regression (10.6.4), which shows that, whereas in the original model the income
variable was statistically insignificant, it is now “highly” significant.
But in dropping a variable from the model we may be committing a 
specification bias
or 
specification error.
Specification bias arises from incorrect specification of the model
used in the analysis. Thus, if economic theory says that income and wealth should both be
included in the model explaining the consumption expenditure, dropping the wealth vari-
able would constitute specification bias.
Although we will discuss the topic of specification bias in Chapter 13, we caught a
glimpse of it in Section 7.7. If, for example, the true model is
Y
i
=
β
1
+
β
2
X
2
i
+
β
3
X
3
i
+
u
i
but we mistakenly fit the model
Y
i
=
b
1
+
b
1 2
X
2
i
+ ˆ
u
i